-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1263481560636553194939824085761', 'a10': [0, 0], 'a2': [0, 2.0], 'a3': [0, 0], 'a4': [-4.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -23.0], 'a8': [0, -8.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 79.65257850774987, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -2.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1350.649', 'coefficient_field': 'CDF', 'conductor': 1350, 'conductor_radical': 30, 'conjugate': '694880275141035009984997070351', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 23.0], [-343.0, 0]], [[1.0, 0], [-30.0, 0], [1331.0, 0]], [[1.0, 0], [0, 34.0], [-2197.0, 0]], [[1.0, 0], [0, -42.0], [-4913.0, 0]], [[1.0, 0], [-139.0, 0], [6859.0, 0]], [[1.0, 0], [0, -192.0], [-12167.0, 0]], [[1.0, 0], [234.0, 0], [24389.0, 0]], [[1.0, 0], [55.0, 0], [29791.0, 0]], [[1.0, 0], [0, 191.0], [-50653.0, 0]], [[1.0, 0], [-138.0, 0], [68921.0, 0]], [[1.0, 0], [0, -53.0], [-79507.0, 0]], [[1.0, 0], [0, 366.0], [-103823.0, 0]], [[1.0, 0], [0, 330.0], [-148877.0, 0]], [[1.0, 0], [-396.0, 0], [205379.0, 0]], [[1.0, 0], [-23.0, 0], [226981.0, 0]], [[1.0, 0], [0, 452.0], [-300763.0, 0]], [[1.0, 0], [-204.0, 0], [357911.0, 0]], [[1.0, 0], [0, 691.0], [-389017.0, 0]], [[1.0, 0], [-709.0, 0], [493039.0, 0]], [[1.0, 0], [0, -1098.0], [-571787.0, 0]], [[1.0, 0], [-816.0, 0], [704969.0, 0]], [[1.0, 0], [0, 905.0], [-912673.0, 0]], [[1.0, 0], [1278.0, 0], [1030301.0, 0]], [[1.0, 0], [0, -605.0], [-1092727.0, 0]], [[1.0, 0], [0, 1488.0], [-1225043.0, 0]], [[1.0, 0], [593.0, 0], [1295029.0, 0]], [[1.0, 0], [0, -324.0], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 54, 'label': '2-1350-5.4-c3-0-54', 'leading_term': '1.948077068551831185767920335915599636544983486495093685', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1350/4/c/p/649/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.9480770685518312, 2.0454678101015604, 2.112969768776289, 2.1496752317777132, 2.155132407797514, 2.1293506225218644, 2.0728037768245673, 1.9864315048753731, 1.8716372546004814, 1.7302823448081561, 1.5646749428734605, 1.3775528624718805, 1.1720591077735254, 0.9517091909551296, 0.7203494229541479, 0.4821056191934901, 0.24132196587235905, 0.0024901491261687396, -0.22983075258647817, -0.4511026865719584, -0.6569039894492542, -0.8430298960420144, -1.0055959793151306, -1.1411419315452493, -1.2467327778159432, -1.3200543674187595, -1.3594998328508505, -1.3642436540853113, -1.3343000294886231, -1.2705624429406377, -1.1748216344601188, -1.0497596297896876, -0.8989180590681647, -0.7266396869739536, -0.5379828723674961, -0.33860955504584234, -0.13464830624816881, 0.06746505110554801, 0.26116577988452666, 0.4399531237123821, 0.5975925085872218, 0.7283210654689858, 0.8270499069986298, 0.8895561995624773, 0.9126579005793365, 0.8943641058560146, 0.8339942915058145, 0.7322603488880213, 0.5913061989863783, 0.4147009234228776, 0.20738274032055923, -0.02444724960769666, -0.2734808633033877, -0.5315056350643259, -0.7896501644574937, -1.0386656873357125, -1.2692357776084333, -1.472304504788842, -1.6394120511175045, -1.7630258045169138, -1.836854354097611, -1.8561316764517217, -1.8178591521050274, -1.7209939135518033, -1.5665734009974224, -1.3577678698106972, -1.0998549132258197, -0.8001127715269655, -0.4676322103245099, -0.11304996217910672, 0.25178998157551685, 0.6142376996862977, 0.9612887078357384, 1.280070056032482, 1.55834358871877, 1.7850071289173588, 1.9505733745617198, 2.047606105002831, 2.0710939456971578, 2.0187434536731805, 1.891175653907673, 1.6920133275662048, 1.4278502391501942, 1.1080979659092625, 0.7447109005245747, 0.35179514920510707, -0.05488776823334325, -0.4585065165073224, -0.8418143689086923, -1.187848057558043, -1.4806435767111181, -1.7059394290335068, -1.851836950858515, -1.9093877830029615, -1.8730803177309885, -1.741200041103085, -1.5160430335904962, -1.203967359720039, -0.8152734803372523, -0.36391191648487914, 0.1329761051570301, 0.6556717095944081, 1.18262448866507, 1.691304303006814, 2.159125613135734, 2.5644066435965693, 2.8873226600209767, 3.110811336678762, 3.2213887483546957, 3.209836990549141, 3.0717287835680533, 2.8077605257988485, 2.423872916923604, 1.9311471773458588, 1.345474677231804, 0.6870080305306354, -0.020588060764635183, -0.7510581950432713, -1.476613123502769, -2.169077980744497, -2.801082327796623, -3.347239128183596, -3.7852588661047735, -4.09694663318089, -4.2690341636204305, -4.293805368981338, -4.169482670640493, -3.9003519913245044, -3.496616183870417, -2.9739793990974017, -2.352977819286467, -1.6580846727001055, -0.9166288621506153, -0.15757628480826202, 0.5897695448760324, 1.2970860721280049, 1.9383060638553005, 2.4907855649745585, 2.9363076418302327, 3.2618715024073173, 3.4602266862682, 3.530124369253936, 3.476271840657345, 3.308991191659902, 3.043598441033322, 2.6995339236376057, 2.2992879954919854, 1.8671772353288043, 1.428034709683108, 1.0058830111938002, 0.6226603351545218, 0.2970676710006767, 0.04359929715033045, -0.1281905732220184, -0.21414449834314064, -0.2156561093734832, -0.1395126151122622, 0.0025667686449942716, 0.19467181704170566, 0.41768128125274184, 0.6504276681423071, 0.8709817195231182, 1.05798411097665, 1.1919485045676617, 1.2564609683014496, 1.2392059442544727, 1.1327581874973882, 0.9350929503173592, 0.6497824730573816, 0.2858647014357206, -0.14261092134563932, -0.6173368267799214, -1.1167583076868879, -1.6172849694640508, -2.094633043506259, -2.5252204473053377, -2.8875324769881607, -3.16337685114713, -3.3389525249076977, -3.4056670040239228, -3.360651271160258, -3.2069390939404703, -2.9532974052227643, -2.613715460009176, -2.2065813188310366, -1.753593606587877, -1.2784732327078387, -0.8055527553684675, -0.3583294596306164, 0.041928606134687546, 0.3774367212426161, 0.6349285870718714, 0.8064061647662621, 0.889555221451653, 0.8877981348389589, 0.809978214942504, 0.6696932381688351, 0.4843185797688592, 0.27378081668444665, 0.05915960284991869, -0.13879216192470475, -0.30111322019711223, -0.4119867573946943, -0.45988976684532196, -0.4384594800203929, -0.3470146246292696, -0.19069094564063221, 0.019824805748222603, 0.26895188858438795, 0.5372268787290784, 0.8026082115166994, 1.0419920568495311, 1.23284171408196, 1.354822910178652, 1.3913344792755378, 1.3308282552671182, 1.1678235133424248, 0.9035393695080233, 0.5460921586060845, 0.11023253795673972, -0.3833728271748087, -0.9092795847029405, -1.4387596271844159, -1.9415607899073213, -2.3878223458002252, -2.750023000947152, -3.004832633570572, -3.1347419948936714, -3.1293560268090124, -2.9862558100505345, -2.7113603560740516, -2.318750929034166, -1.8299553698473816, -1.2727257572412187, -0.6793773140319427, -0.08478740694367702, 0.4758213677206581, 0.9691725042169154, 1.3661512859648552, 1.6437961150825535, 1.7869279692874982, 1.7893011915927688, 1.6541878444978917, 1.3943434677978293, 1.0313420447753234, 0.5943097329119037, 0.11812769490022308, -0.3587885872426049, -0.7969953956022896, -1.1586519276179084, -1.4101041958572897, -1.5242486338673655, -1.4825132187595134, -1.276315885566561, -0.9078918570354777, -0.39042132144781044, 0.2525658463360375], 'positive_zeros': ['0.996711207653808070261584069648531', '2.14823276783165838146648620826159', '2.98233355757029309152521709874329', '4.06120804337144436867189475943513', '5.03118314197903679268832560075158', '5.84408649574187243833065410715366', '6.79520705165701299812025387109836', '7.80517189333905903915727446339893', '8.918711807810749363964605666696997', '9.198332325488581750882798452469973'], 'prelabel': '2-1350-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.924829326533358, 'root_angle': 0.14758361765043326, 'root_number': '0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07379180882521663', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.996711207653808070261584069649', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.14823276783165838146648620826', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98233355757029309152521709874', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 79.65257850774987, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 1350, 'conductor_radical': 30, 'degree': 2, 'index': 54, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1350/4/c/p/649/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-1350-5.4-c3-0-54', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1350-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.924829326533358, 'root_angle': 0.07379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.996711207653808070261584069649', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1263481560636553194939824085761', 'Lhash_array': ['1263481560636553194939824085761'], 'label': '2-1350-5.4-c3-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1350/4/c/p/649/2'}